Question: s involving definite integrals (algebraic) AP.CALC: CHA‑4 (EU), CHA‑4.D (LO), CHA‑4.D.1 (EK), CHA‑4.D.2 (EK), CHA‑4.E (LO), CHA‑4.E.1 (EK) Google Classroom Facebook Twitter Email You might need: Calculator Problem The work done by stretching a certain spring increases by $0.13x$ joules per centimeter (where $x$ is the displacement, in centimeters, beyond the spring's natural length). How much work (in Joules) must be done in order to stretch the spring from $x=4$ to $x=10$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $5.46$ (Choice B) B $7.54$ (Choice C) C $10.92$ (Choice D) D $15.08$
Solution: Letting $W(x)$ be the work done stretching a spring $x$ centimeters beyond its natural length, we are given that $W'(x)=0.13x$. We want to find $W(10)-W(4)$. According to the Fundamental Theorem of Calculus, $\begin{aligned} W(10)-W(4)&=\int_{4}^{10} W'(x)\,dx \\\\ &=\int_{4}^{10}(0.13x)\,dx \end{aligned}$ $\int_{4}^{10}(0.13x)\,dx=5.46$ In conclusion, to stretch the spring from $x=4$ to $x=10$ the work done is $5.46$ joules.